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# 黑塞二十七面体

## 维基百科，自由的百科全书

27 3{3}3
72 3{}英语Trion (geometry)

(0,ωλ,−ωμ)
(−ωμ,0,ωλ)
λ,−ωμ,0)

E6
[12]
Aut(E6)
[18/2]
D5
[8]
D4 / A2
[6]

(1=红,3=橘)

(1)

(1,3)

(3,9)
B6
[12/2]
A5
[6]
A4
[5]
A3 / D3
[4]

(1,3)

(1,3)

(1,2)

(1,4,7)

## 注释

1. ^ 数学中，边或通常可以代表顶点皆只位在单一轴上并不涉及其他轴分量组成的几何结构，例如x轴上的(2,0)连接到(3,0)的棱，但若将每一个维度从实数推广至复数，则“轴”的概念可以被替换为高斯平面，这意味着棱不再只是一条线段，而可能是高斯平面上的一个区域。而三元边或三元棱则为连接三个顶点所构成复数空间的棱。这种结构无法存于实空间，在实空间中，三元棱对应的几何结构为三角形
2. 对偶多面体为本身的多面体称为自身对偶多面体

## 参考文献

1. Coxeter, H. S. M., Moser, W. O. J.; Generators and Relations for Discrete Groups (1965), esp pp 67–80.
2. Coxeter, H. S. M.; Regular Complex Polytopes, Cambridge University Press, (1974).
3. Coxeter, H. S. M., Shephard, G.C.; Portraits of a family of complex polytopes, Leonardo Vol 25, No 3/4, (1992), pp 239–244,
1. Stacey, Blake C, Sporadic SICs and Exceptional Lie Algebras, sunclipse, December 30, 2018
2. Duke, Andrew Cameron, Cube-like regular incidence complexes, Northeastern University, 2014
3. ^ Krishnan, R and Harrison, PF and Scott, WG. Fully constrained Majorana neutrino mass matrices using ${\displaystyle {\mathit {\Sigma ))(72\times 3)}$. The European Physical Journal C (Springer). 2018, 78 (1): 74.
4. Coxeter, H.S.M., Regular Complex Polytopes, Cambridge University Press, 1991, ISBN 0-521-39490-2
5. ^ Coxeter, Complex Regular polytopes,[4] p.123
6. Briand, Emmanuel and Luque, Jean-Gabriel and Thibon, Jean-Yves and Verstraete, Frank. The moduli space of three-qutrit states. Journal of mathematical physics (AIP). 2004, 45 (12): 4855––4867.
7. ^ Complex Regular Polytopes,[4] 11.1 Regular complex polygons p.103
8. ^ Coxeter, HSM. The equianharmonic surface and the Hessian polyhedron. Annali di Matematica Pura ed Applicata (Springer). 1974, 98 (1): 77––92.
9. ^ Complex Regular Polytopes,[4] 11.1 Regular complex polygons p.103
10. ^ de Wet, JA, A Standard Model Algebra, International Mathematical Forum, 2012, 7 (51): 2519––2524
11. ^ Lei, Y. Hessian Polyhedra, Invariant Theory and Appell Hypergeometric Functions. World Scientific Publishing Company. 2018: p.127. ISBN 9789813209497.